Properties

Label 605.2.g.d.251.1
Level $605$
Weight $2$
Character 605.251
Analytic conductor $4.831$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 251.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 605.251
Dual form 605.2.g.d.511.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(2.42705 - 1.76336i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.927051 + 2.85317i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(1.85410 - 5.70634i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(2.42705 - 1.76336i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(0.927051 + 2.85317i) q^{6} +(2.42705 + 1.76336i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(1.85410 - 5.70634i) q^{9} -1.00000 q^{10} +3.00000 q^{12} +(1.23607 - 3.80423i) q^{13} +(-2.42705 + 1.76336i) q^{14} +(2.42705 + 1.76336i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(4.85410 + 3.52671i) q^{18} +(-3.23607 + 2.35114i) q^{19} +(-0.309017 + 0.951057i) q^{20} +9.00000 q^{21} -8.00000 q^{23} +(-2.78115 + 8.55951i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(3.23607 + 2.35114i) q^{26} +(-2.78115 - 8.55951i) q^{27} +(0.927051 + 2.85317i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-2.42705 + 1.76336i) q^{30} +(-0.618034 + 1.90211i) q^{31} -5.00000 q^{32} +(-0.927051 + 2.85317i) q^{35} +(4.85410 - 3.52671i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-1.23607 - 3.80423i) q^{38} +(-3.70820 - 11.4127i) q^{39} +(-2.42705 - 1.76336i) q^{40} +(4.04508 - 2.93893i) q^{41} +(-2.78115 + 8.55951i) q^{42} +5.00000 q^{43} +6.00000 q^{45} +(2.47214 - 7.60845i) q^{46} +(2.42705 - 1.76336i) q^{47} +(-2.42705 - 1.76336i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(3.23607 - 2.35114i) q^{52} +(1.23607 - 3.80423i) q^{53} +9.00000 q^{54} -9.00000 q^{56} +(-3.70820 + 11.4127i) q^{57} +(4.85410 - 3.52671i) q^{58} +(1.61803 + 1.17557i) q^{59} +(0.927051 + 2.85317i) q^{60} +(-3.39919 - 10.4616i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(14.5623 - 10.5801i) q^{63} +(2.16312 - 6.65740i) q^{64} +4.00000 q^{65} -13.0000 q^{67} +(-19.4164 + 14.1068i) q^{69} +(-2.42705 - 1.76336i) q^{70} +(0.618034 + 1.90211i) q^{71} +(5.56231 + 17.1190i) q^{72} +(6.47214 + 4.70228i) q^{73} +(-6.47214 + 4.70228i) q^{74} +(-0.927051 + 2.85317i) q^{75} -4.00000 q^{76} +12.0000 q^{78} +(3.09017 - 9.51057i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-7.28115 - 5.29007i) q^{81} +(1.54508 + 4.75528i) q^{82} +(1.23607 + 3.80423i) q^{83} +(7.28115 + 5.29007i) q^{84} +(-1.54508 + 4.75528i) q^{86} -18.0000 q^{87} +1.00000 q^{89} +(-1.85410 + 5.70634i) q^{90} +(9.70820 - 7.05342i) q^{91} +(-6.47214 - 4.70228i) q^{92} +(1.85410 + 5.70634i) q^{93} +(0.927051 + 2.85317i) q^{94} +(-3.23607 - 2.35114i) q^{95} +(-12.1353 + 8.81678i) q^{96} +(-2.47214 + 7.60845i) q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 3q^{3} + q^{4} - q^{5} - 3q^{6} + 3q^{7} - 3q^{8} - 6q^{9} + O(q^{10}) \) \( 4q + q^{2} + 3q^{3} + q^{4} - q^{5} - 3q^{6} + 3q^{7} - 3q^{8} - 6q^{9} - 4q^{10} + 12q^{12} - 4q^{13} - 3q^{14} + 3q^{15} + q^{16} + 6q^{18} - 4q^{19} + q^{20} + 36q^{21} - 32q^{23} + 9q^{24} - q^{25} + 4q^{26} + 9q^{27} - 3q^{28} - 6q^{29} - 3q^{30} + 2q^{31} - 20q^{32} + 3q^{35} + 6q^{36} + 8q^{37} + 4q^{38} + 12q^{39} - 3q^{40} + 5q^{41} + 9q^{42} + 20q^{43} + 24q^{45} - 8q^{46} + 3q^{47} - 3q^{48} - 2q^{49} + q^{50} + 4q^{52} - 4q^{53} + 36q^{54} - 36q^{56} + 12q^{57} + 6q^{58} + 2q^{59} - 3q^{60} + 11q^{61} - 2q^{62} + 18q^{63} - 7q^{64} + 16q^{65} - 52q^{67} - 24q^{69} - 3q^{70} - 2q^{71} - 18q^{72} + 8q^{73} - 8q^{74} + 3q^{75} - 16q^{76} + 48q^{78} - 10q^{79} + q^{80} - 9q^{81} - 5q^{82} - 4q^{83} + 9q^{84} + 5q^{86} - 72q^{87} + 4q^{89} + 6q^{90} + 12q^{91} - 8q^{92} - 6q^{93} - 3q^{94} - 4q^{95} - 15q^{96} + 8q^{97} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i 0.780378 + 0.625308i \(0.215027\pi\)
−0.998886 + 0.0471903i \(0.984973\pi\)
\(3\) 2.42705 1.76336i 1.40126 1.01807i 0.406737 0.913545i \(-0.366667\pi\)
0.994522 0.104528i \(-0.0333333\pi\)
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) 0.927051 + 2.85317i 0.378467 + 1.16480i
\(7\) 2.42705 + 1.76336i 0.917339 + 0.666486i 0.942860 0.333188i \(-0.108125\pi\)
−0.0255212 + 0.999674i \(0.508125\pi\)
\(8\) −2.42705 + 1.76336i −0.858092 + 0.623440i
\(9\) 1.85410 5.70634i 0.618034 1.90211i
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) 3.00000 0.866025
\(13\) 1.23607 3.80423i 0.342824 1.05510i −0.619915 0.784669i \(-0.712833\pi\)
0.962739 0.270434i \(-0.0871670\pi\)
\(14\) −2.42705 + 1.76336i −0.648657 + 0.471277i
\(15\) 2.42705 + 1.76336i 0.626662 + 0.455296i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(18\) 4.85410 + 3.52671i 1.14412 + 0.831254i
\(19\) −3.23607 + 2.35114i −0.742405 + 0.539389i −0.893463 0.449136i \(-0.851732\pi\)
0.151058 + 0.988525i \(0.451732\pi\)
\(20\) −0.309017 + 0.951057i −0.0690983 + 0.212663i
\(21\) 9.00000 1.96396
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) −2.78115 + 8.55951i −0.567700 + 1.74720i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) 3.23607 + 2.35114i 0.634645 + 0.461097i
\(27\) −2.78115 8.55951i −0.535233 1.64728i
\(28\) 0.927051 + 2.85317i 0.175196 + 0.539198i
\(29\) −4.85410 3.52671i −0.901384 0.654894i 0.0374370 0.999299i \(-0.488081\pi\)
−0.938821 + 0.344405i \(0.888081\pi\)
\(30\) −2.42705 + 1.76336i −0.443117 + 0.321943i
\(31\) −0.618034 + 1.90211i −0.111002 + 0.341630i −0.991092 0.133177i \(-0.957482\pi\)
0.880090 + 0.474807i \(0.157482\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 0 0
\(35\) −0.927051 + 2.85317i −0.156700 + 0.482274i
\(36\) 4.85410 3.52671i 0.809017 0.587785i
\(37\) 6.47214 + 4.70228i 1.06401 + 0.773050i 0.974827 0.222965i \(-0.0715734\pi\)
0.0891861 + 0.996015i \(0.471573\pi\)
\(38\) −1.23607 3.80423i −0.200517 0.617127i
\(39\) −3.70820 11.4127i −0.593788 1.82749i
\(40\) −2.42705 1.76336i −0.383750 0.278811i
\(41\) 4.04508 2.93893i 0.631736 0.458983i −0.225265 0.974298i \(-0.572325\pi\)
0.857001 + 0.515314i \(0.172325\pi\)
\(42\) −2.78115 + 8.55951i −0.429141 + 1.32076i
\(43\) 5.00000 0.762493 0.381246 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) 2.47214 7.60845i 0.364497 1.12181i
\(47\) 2.42705 1.76336i 0.354022 0.257212i −0.396533 0.918021i \(-0.629787\pi\)
0.750554 + 0.660809i \(0.229787\pi\)
\(48\) −2.42705 1.76336i −0.350315 0.254518i
\(49\) 0.618034 + 1.90211i 0.0882906 + 0.271730i
\(50\) −0.309017 0.951057i −0.0437016 0.134500i
\(51\) 0 0
\(52\) 3.23607 2.35114i 0.448762 0.326045i
\(53\) 1.23607 3.80423i 0.169787 0.522551i −0.829570 0.558403i \(-0.811414\pi\)
0.999357 + 0.0358519i \(0.0114145\pi\)
\(54\) 9.00000 1.22474
\(55\) 0 0
\(56\) −9.00000 −1.20268
\(57\) −3.70820 + 11.4127i −0.491164 + 1.51165i
\(58\) 4.85410 3.52671i 0.637375 0.463080i
\(59\) 1.61803 + 1.17557i 0.210650 + 0.153046i 0.688108 0.725608i \(-0.258442\pi\)
−0.477458 + 0.878655i \(0.658442\pi\)
\(60\) 0.927051 + 2.85317i 0.119682 + 0.368343i
\(61\) −3.39919 10.4616i −0.435221 1.33947i −0.892860 0.450335i \(-0.851305\pi\)
0.457638 0.889138i \(-0.348695\pi\)
\(62\) −1.61803 1.17557i −0.205491 0.149298i
\(63\) 14.5623 10.5801i 1.83468 1.33297i
\(64\) 2.16312 6.65740i 0.270390 0.832174i
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −13.0000 −1.58820 −0.794101 0.607785i \(-0.792058\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0 0
\(69\) −19.4164 + 14.1068i −2.33746 + 1.69826i
\(70\) −2.42705 1.76336i −0.290088 0.210761i
\(71\) 0.618034 + 1.90211i 0.0733471 + 0.225739i 0.981009 0.193963i \(-0.0621343\pi\)
−0.907662 + 0.419703i \(0.862134\pi\)
\(72\) 5.56231 + 17.1190i 0.655524 + 2.01750i
\(73\) 6.47214 + 4.70228i 0.757506 + 0.550360i 0.898144 0.439701i \(-0.144915\pi\)
−0.140638 + 0.990061i \(0.544915\pi\)
\(74\) −6.47214 + 4.70228i −0.752371 + 0.546629i
\(75\) −0.927051 + 2.85317i −0.107047 + 0.329456i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 12.0000 1.35873
\(79\) 3.09017 9.51057i 0.347671 1.07002i −0.612467 0.790496i \(-0.709823\pi\)
0.960138 0.279526i \(-0.0901773\pi\)
\(80\) 0.809017 0.587785i 0.0904508 0.0657164i
\(81\) −7.28115 5.29007i −0.809017 0.587785i
\(82\) 1.54508 + 4.75528i 0.170626 + 0.525133i
\(83\) 1.23607 + 3.80423i 0.135676 + 0.417568i 0.995695 0.0926948i \(-0.0295481\pi\)
−0.860018 + 0.510263i \(0.829548\pi\)
\(84\) 7.28115 + 5.29007i 0.794439 + 0.577194i
\(85\) 0 0
\(86\) −1.54508 + 4.75528i −0.166611 + 0.512775i
\(87\) −18.0000 −1.92980
\(88\) 0 0
\(89\) 1.00000 0.106000 0.0529999 0.998595i \(-0.483122\pi\)
0.0529999 + 0.998595i \(0.483122\pi\)
\(90\) −1.85410 + 5.70634i −0.195440 + 0.601501i
\(91\) 9.70820 7.05342i 1.01770 0.739400i
\(92\) −6.47214 4.70228i −0.674767 0.490247i
\(93\) 1.85410 + 5.70634i 0.192261 + 0.591720i
\(94\) 0.927051 + 2.85317i 0.0956180 + 0.294282i
\(95\) −3.23607 2.35114i −0.332014 0.241222i
\(96\) −12.1353 + 8.81678i −1.23855 + 0.899859i
\(97\) −2.47214 + 7.60845i −0.251007 + 0.772521i 0.743583 + 0.668644i \(0.233125\pi\)
−0.994590 + 0.103877i \(0.966875\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −1.54508 + 4.75528i −0.153742 + 0.473168i −0.998031 0.0627190i \(-0.980023\pi\)
0.844290 + 0.535887i \(0.180023\pi\)
\(102\) 0 0
\(103\) −6.47214 4.70228i −0.637719 0.463330i 0.221347 0.975195i \(-0.428955\pi\)
−0.859066 + 0.511865i \(0.828955\pi\)
\(104\) 3.70820 + 11.4127i 0.363619 + 1.11911i
\(105\) 2.78115 + 8.55951i 0.271413 + 0.835323i
\(106\) 3.23607 + 2.35114i 0.314315 + 0.228363i
\(107\) −7.28115 + 5.29007i −0.703896 + 0.511410i −0.881199 0.472746i \(-0.843263\pi\)
0.177303 + 0.984156i \(0.443263\pi\)
\(108\) 2.78115 8.55951i 0.267617 0.823639i
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) 0 0
\(111\) 24.0000 2.27798
\(112\) 0.927051 2.85317i 0.0875981 0.269599i
\(113\) −4.85410 + 3.52671i −0.456636 + 0.331765i −0.792210 0.610249i \(-0.791070\pi\)
0.335575 + 0.942014i \(0.391070\pi\)
\(114\) −9.70820 7.05342i −0.909257 0.660614i
\(115\) −2.47214 7.60845i −0.230528 0.709492i
\(116\) −1.85410 5.70634i −0.172149 0.529820i
\(117\) −19.4164 14.1068i −1.79505 1.30418i
\(118\) −1.61803 + 1.17557i −0.148952 + 0.108220i
\(119\) 0 0
\(120\) −9.00000 −0.821584
\(121\) 0 0
\(122\) 11.0000 0.995893
\(123\) 4.63525 14.2658i 0.417947 1.28631i
\(124\) −1.61803 + 1.17557i −0.145304 + 0.105569i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) 5.56231 + 17.1190i 0.495530 + 1.52508i
\(127\) 3.39919 + 10.4616i 0.301629 + 0.928319i 0.980914 + 0.194444i \(0.0622902\pi\)
−0.679285 + 0.733875i \(0.737710\pi\)
\(128\) −2.42705 1.76336i −0.214523 0.155860i
\(129\) 12.1353 8.81678i 1.06845 0.776274i
\(130\) −1.23607 + 3.80423i −0.108410 + 0.333653i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) 4.01722 12.3637i 0.347035 1.06806i
\(135\) 7.28115 5.29007i 0.626662 0.455296i
\(136\) 0 0
\(137\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(138\) −7.41641 22.8254i −0.631327 1.94302i
\(139\) 14.5623 + 10.5801i 1.23516 + 0.897395i 0.997266 0.0738961i \(-0.0235433\pi\)
0.237893 + 0.971291i \(0.423543\pi\)
\(140\) −2.42705 + 1.76336i −0.205123 + 0.149031i
\(141\) 2.78115 8.55951i 0.234215 0.720841i
\(142\) −2.00000 −0.167836
\(143\) 0 0
\(144\) −6.00000 −0.500000
\(145\) 1.85410 5.70634i 0.153975 0.473886i
\(146\) −6.47214 + 4.70228i −0.535638 + 0.389164i
\(147\) 4.85410 + 3.52671i 0.400360 + 0.290878i
\(148\) 2.47214 + 7.60845i 0.203208 + 0.625411i
\(149\) −5.25329 16.1680i −0.430366 1.32453i −0.897761 0.440482i \(-0.854807\pi\)
0.467395 0.884049i \(-0.345193\pi\)
\(150\) −2.42705 1.76336i −0.198168 0.143977i
\(151\) 11.3262 8.22899i 0.921716 0.669666i −0.0222344 0.999753i \(-0.507078\pi\)
0.943951 + 0.330087i \(0.107078\pi\)
\(152\) 3.70820 11.4127i 0.300775 0.925690i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 3.70820 11.4127i 0.296894 0.913746i
\(157\) 6.47214 4.70228i 0.516533 0.375283i −0.298763 0.954327i \(-0.596574\pi\)
0.815296 + 0.579044i \(0.196574\pi\)
\(158\) 8.09017 + 5.87785i 0.643619 + 0.467617i
\(159\) −3.70820 11.4127i −0.294080 0.905084i
\(160\) −1.54508 4.75528i −0.122150 0.375938i
\(161\) −19.4164 14.1068i −1.53023 1.11178i
\(162\) 7.28115 5.29007i 0.572061 0.415627i
\(163\) −5.25329 + 16.1680i −0.411469 + 1.26637i 0.503902 + 0.863761i \(0.331897\pi\)
−0.915371 + 0.402611i \(0.868103\pi\)
\(164\) 5.00000 0.390434
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) −2.16312 + 6.65740i −0.167387 + 0.515165i −0.999204 0.0398851i \(-0.987301\pi\)
0.831817 + 0.555050i \(0.187301\pi\)
\(168\) −21.8435 + 15.8702i −1.68526 + 1.22441i
\(169\) −2.42705 1.76336i −0.186696 0.135643i
\(170\) 0 0
\(171\) 7.41641 + 22.8254i 0.567147 + 1.74550i
\(172\) 4.04508 + 2.93893i 0.308435 + 0.224091i
\(173\) −19.4164 + 14.1068i −1.47620 + 1.07252i −0.497446 + 0.867495i \(0.665729\pi\)
−0.978756 + 0.205029i \(0.934271\pi\)
\(174\) 5.56231 17.1190i 0.421677 1.29779i
\(175\) −3.00000 −0.226779
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) −0.309017 + 0.951057i −0.0231618 + 0.0712847i
\(179\) 21.0344 15.2824i 1.57219 1.14226i 0.647165 0.762350i \(-0.275954\pi\)
0.925023 0.379912i \(-0.124046\pi\)
\(180\) 4.85410 + 3.52671i 0.361803 + 0.262866i
\(181\) −5.87132 18.0701i −0.436412 1.34314i −0.891633 0.452759i \(-0.850440\pi\)
0.455221 0.890379i \(-0.349560\pi\)
\(182\) 3.70820 + 11.4127i 0.274870 + 0.845964i
\(183\) −26.6976 19.3969i −1.97354 1.43386i
\(184\) 19.4164 14.1068i 1.43140 1.03997i
\(185\) −2.47214 + 7.60845i −0.181755 + 0.559385i
\(186\) −6.00000 −0.439941
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 8.34346 25.6785i 0.606897 1.86784i
\(190\) 3.23607 2.35114i 0.234769 0.170570i
\(191\) −6.47214 4.70228i −0.468307 0.340245i 0.328474 0.944513i \(-0.393466\pi\)
−0.796781 + 0.604268i \(0.793466\pi\)
\(192\) −6.48936 19.9722i −0.468329 1.44137i
\(193\) −3.09017 9.51057i −0.222435 0.684585i −0.998542 0.0539836i \(-0.982808\pi\)
0.776107 0.630602i \(-0.217192\pi\)
\(194\) −6.47214 4.70228i −0.464672 0.337604i
\(195\) 9.70820 7.05342i 0.695219 0.505106i
\(196\) −0.618034 + 1.90211i −0.0441453 + 0.135865i
\(197\) −14.0000 −0.997459 −0.498729 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(198\) 0 0
\(199\) −6.00000 −0.425329 −0.212664 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) 0.927051 2.85317i 0.0655524 0.201750i
\(201\) −31.5517 + 22.9236i −2.22548 + 1.61691i
\(202\) −4.04508 2.93893i −0.284611 0.206782i
\(203\) −5.56231 17.1190i −0.390397 1.20152i
\(204\) 0 0
\(205\) 4.04508 + 2.93893i 0.282521 + 0.205264i
\(206\) 6.47214 4.70228i 0.450935 0.327624i
\(207\) −14.8328 + 45.6507i −1.03095 + 3.17294i
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) −9.00000 −0.621059
\(211\) −6.79837 + 20.9232i −0.468019 + 1.44042i 0.387126 + 0.922027i \(0.373468\pi\)
−0.855145 + 0.518389i \(0.826532\pi\)
\(212\) 3.23607 2.35114i 0.222254 0.161477i
\(213\) 4.85410 + 3.52671i 0.332598 + 0.241646i
\(214\) −2.78115 8.55951i −0.190116 0.585116i
\(215\) 1.54508 + 4.75528i 0.105374 + 0.324308i
\(216\) 21.8435 + 15.8702i 1.48626 + 1.07983i
\(217\) −4.85410 + 3.52671i −0.329518 + 0.239409i
\(218\) 2.78115 8.55951i 0.188363 0.579723i
\(219\) 24.0000 1.62177
\(220\) 0 0
\(221\) 0 0
\(222\) −7.41641 + 22.8254i −0.497757 + 1.53194i
\(223\) −4.04508 + 2.93893i −0.270879 + 0.196805i −0.714929 0.699197i \(-0.753541\pi\)
0.444050 + 0.896002i \(0.353541\pi\)
\(224\) −12.1353 8.81678i −0.810821 0.589096i
\(225\) 1.85410 + 5.70634i 0.123607 + 0.380423i
\(226\) −1.85410 5.70634i −0.123333 0.379580i
\(227\) 0.809017 + 0.587785i 0.0536963 + 0.0390127i 0.614310 0.789065i \(-0.289435\pi\)
−0.560613 + 0.828078i \(0.689435\pi\)
\(228\) −9.70820 + 7.05342i −0.642942 + 0.467124i
\(229\) −0.309017 + 0.951057i −0.0204204 + 0.0628476i −0.960747 0.277424i \(-0.910519\pi\)
0.940327 + 0.340272i \(0.110519\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 18.0000 1.18176
\(233\) −7.41641 + 22.8254i −0.485865 + 1.49534i 0.344859 + 0.938654i \(0.387927\pi\)
−0.830724 + 0.556684i \(0.812073\pi\)
\(234\) 19.4164 14.1068i 1.26929 0.922193i
\(235\) 2.42705 + 1.76336i 0.158323 + 0.115029i
\(236\) 0.618034 + 1.90211i 0.0402306 + 0.123817i
\(237\) −9.27051 28.5317i −0.602184 1.85333i
\(238\) 0 0
\(239\) −3.23607 + 2.35114i −0.209324 + 0.152083i −0.687508 0.726177i \(-0.741295\pi\)
0.478184 + 0.878260i \(0.341295\pi\)
\(240\) 0.927051 2.85317i 0.0598409 0.184171i
\(241\) 23.0000 1.48156 0.740780 0.671748i \(-0.234456\pi\)
0.740780 + 0.671748i \(0.234456\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 3.39919 10.4616i 0.217611 0.669737i
\(245\) −1.61803 + 1.17557i −0.103372 + 0.0751044i
\(246\) 12.1353 + 8.81678i 0.773716 + 0.562137i
\(247\) 4.94427 + 15.2169i 0.314596 + 0.968228i
\(248\) −1.85410 5.70634i −0.117736 0.362353i
\(249\) 9.70820 + 7.05342i 0.615232 + 0.446993i
\(250\) 0.809017 0.587785i 0.0511667 0.0371748i
\(251\) 5.56231 17.1190i 0.351090 1.08054i −0.607153 0.794585i \(-0.707688\pi\)
0.958242 0.285958i \(-0.0923116\pi\)
\(252\) 18.0000 1.13389
\(253\) 0 0
\(254\) −11.0000 −0.690201
\(255\) 0 0
\(256\) 13.7533 9.99235i 0.859581 0.624522i
\(257\) 4.85410 + 3.52671i 0.302791 + 0.219990i 0.728797 0.684730i \(-0.240080\pi\)
−0.426006 + 0.904720i \(0.640080\pi\)
\(258\) 4.63525 + 14.2658i 0.288578 + 0.888153i
\(259\) 7.41641 + 22.8254i 0.460833 + 1.41830i
\(260\) 3.23607 + 2.35114i 0.200692 + 0.145812i
\(261\) −29.1246 + 21.1603i −1.80277 + 1.30979i
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 3.70820 11.4127i 0.227365 0.699756i
\(267\) 2.42705 1.76336i 0.148533 0.107916i
\(268\) −10.5172 7.64121i −0.642442 0.466761i
\(269\) 6.48936 + 19.9722i 0.395663 + 1.21773i 0.928444 + 0.371472i \(0.121147\pi\)
−0.532781 + 0.846253i \(0.678853\pi\)
\(270\) 2.78115 + 8.55951i 0.169256 + 0.520915i
\(271\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(272\) 0 0
\(273\) 11.1246 34.2380i 0.673292 2.07218i
\(274\) 0 0
\(275\) 0 0
\(276\) −24.0000 −1.44463
\(277\) 4.32624 13.3148i 0.259938 0.800008i −0.732878 0.680360i \(-0.761823\pi\)
0.992816 0.119648i \(-0.0381766\pi\)
\(278\) −14.5623 + 10.5801i −0.873389 + 0.634554i
\(279\) 9.70820 + 7.05342i 0.581215 + 0.422277i
\(280\) −2.78115 8.55951i −0.166206 0.511528i
\(281\) −1.85410 5.70634i −0.110606 0.340412i 0.880399 0.474234i \(-0.157275\pi\)
−0.991005 + 0.133822i \(0.957275\pi\)
\(282\) 7.28115 + 5.29007i 0.433586 + 0.315019i
\(283\) 10.5172 7.64121i 0.625184 0.454223i −0.229545 0.973298i \(-0.573724\pi\)
0.854728 + 0.519075i \(0.173724\pi\)
\(284\) −0.618034 + 1.90211i −0.0366736 + 0.112870i
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 15.0000 0.885422
\(288\) −9.27051 + 28.5317i −0.546270 + 1.68125i
\(289\) 13.7533 9.99235i 0.809017 0.587785i
\(290\) 4.85410 + 3.52671i 0.285043 + 0.207096i
\(291\) 7.41641 + 22.8254i 0.434758 + 1.33805i
\(292\) 2.47214 + 7.60845i 0.144671 + 0.445251i
\(293\) 27.5066 + 19.9847i 1.60695 + 1.16752i 0.872153 + 0.489233i \(0.162723\pi\)
0.734798 + 0.678286i \(0.237277\pi\)
\(294\) −4.85410 + 3.52671i −0.283097 + 0.205682i
\(295\) −0.618034 + 1.90211i −0.0359833 + 0.110745i
\(296\) −24.0000 −1.39497
\(297\) 0 0
\(298\) 17.0000 0.984784
\(299\) −9.88854 + 30.4338i −0.571869 + 1.76003i
\(300\) −2.42705 + 1.76336i −0.140126 + 0.101807i
\(301\) 12.1353 + 8.81678i 0.699464 + 0.508191i
\(302\) 4.32624 + 13.3148i 0.248947 + 0.766180i
\(303\) 4.63525 + 14.2658i 0.266288 + 0.819552i
\(304\) 3.23607 + 2.35114i 0.185601 + 0.134847i
\(305\) 8.89919 6.46564i 0.509566 0.370221i
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) −24.0000 −1.36531
\(310\) 0.618034 1.90211i 0.0351020 0.108033i
\(311\) −19.4164 + 14.1068i −1.10100 + 0.799926i −0.981223 0.192875i \(-0.938219\pi\)
−0.119780 + 0.992800i \(0.538219\pi\)
\(312\) 29.1246 + 21.1603i 1.64886 + 1.19796i
\(313\) 2.47214 + 7.60845i 0.139733 + 0.430055i 0.996296 0.0859876i \(-0.0274046\pi\)
−0.856563 + 0.516043i \(0.827405\pi\)
\(314\) 2.47214 + 7.60845i 0.139511 + 0.429370i
\(315\) 14.5623 + 10.5801i 0.820493 + 0.596123i
\(316\) 8.09017 5.87785i 0.455108 0.330655i
\(317\) 5.56231 17.1190i 0.312410 0.961500i −0.664397 0.747380i \(-0.731312\pi\)
0.976807 0.214120i \(-0.0686884\pi\)
\(318\) 12.0000 0.672927
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) −8.34346 + 25.6785i −0.465686 + 1.43324i
\(322\) 19.4164 14.1068i 1.08203 0.786144i
\(323\) 0 0
\(324\) −2.78115 8.55951i −0.154508 0.475528i
\(325\) 1.23607 + 3.80423i 0.0685647 + 0.211020i
\(326\) −13.7533 9.99235i −0.761724 0.553425i
\(327\) −21.8435 + 15.8702i −1.20795 + 0.877624i
\(328\) −4.63525 + 14.2658i −0.255939 + 0.787700i
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −1.23607 + 3.80423i −0.0678380 + 0.208784i
\(333\) 38.8328 28.2137i 2.12803 1.54610i
\(334\) −5.66312 4.11450i −0.309872 0.225135i
\(335\) −4.01722 12.3637i −0.219484 0.675503i
\(336\) −2.78115 8.55951i −0.151724 0.466959i
\(337\) 9.70820 + 7.05342i 0.528840 + 0.384224i 0.819924 0.572473i \(-0.194016\pi\)
−0.291084 + 0.956698i \(0.594016\pi\)
\(338\) 2.42705 1.76336i 0.132014 0.0959139i
\(339\) −5.56231 + 17.1190i −0.302103 + 0.929777i
\(340\) 0 0
\(341\) 0 0
\(342\) −24.0000 −1.29777
\(343\) 4.63525 14.2658i 0.250280 0.770283i
\(344\) −12.1353 + 8.81678i −0.654289 + 0.475369i
\(345\) −19.4164 14.1068i −1.04534 0.759487i
\(346\) −7.41641 22.8254i −0.398709 1.22710i
\(347\) 2.16312 + 6.65740i 0.116122 + 0.357388i 0.992179 0.124820i \(-0.0398352\pi\)
−0.876057 + 0.482207i \(0.839835\pi\)
\(348\) −14.5623 10.5801i −0.780622 0.567155i
\(349\) −17.7984 + 12.9313i −0.952725 + 0.692195i −0.951450 0.307804i \(-0.900406\pi\)
−0.00127528 + 0.999999i \(0.500406\pi\)
\(350\) 0.927051 2.85317i 0.0495530 0.152508i
\(351\) −36.0000 −1.92154
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) −1.85410 + 5.70634i −0.0985444 + 0.303289i
\(355\) −1.61803 + 1.17557i −0.0858763 + 0.0623928i
\(356\) 0.809017 + 0.587785i 0.0428778 + 0.0311526i
\(357\) 0 0
\(358\) 8.03444 + 24.7275i 0.424633 + 1.30689i
\(359\) 22.6525 + 16.4580i 1.19555 + 0.868619i 0.993840 0.110826i \(-0.0353495\pi\)
0.201712 + 0.979445i \(0.435349\pi\)
\(360\) −14.5623 + 10.5801i −0.767501 + 0.557622i
\(361\) −0.927051 + 2.85317i −0.0487922 + 0.150167i
\(362\) 19.0000 0.998618
\(363\) 0 0
\(364\) 12.0000 0.628971
\(365\) −2.47214 + 7.60845i −0.129398 + 0.398245i
\(366\) 26.6976 19.3969i 1.39550 1.01389i
\(367\) −0.809017 0.587785i −0.0422303 0.0306821i 0.566470 0.824082i \(-0.308309\pi\)
−0.608700 + 0.793400i \(0.708309\pi\)
\(368\) 2.47214 + 7.60845i 0.128869 + 0.396618i
\(369\) −9.27051 28.5317i −0.482603 1.48530i
\(370\) −6.47214 4.70228i −0.336470 0.244460i
\(371\) 9.70820 7.05342i 0.504025 0.366195i
\(372\) −1.85410 + 5.70634i −0.0961307 + 0.295860i
\(373\) 18.0000 0.932005 0.466002 0.884783i \(-0.345694\pi\)
0.466002 + 0.884783i \(0.345694\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) −2.78115 + 8.55951i −0.143427 + 0.441423i
\(377\) −19.4164 + 14.1068i −0.999996 + 0.726540i
\(378\) 21.8435 + 15.8702i 1.12351 + 0.816275i
\(379\) −6.79837 20.9232i −0.349209 1.07475i −0.959292 0.282417i \(-0.908864\pi\)
0.610083 0.792338i \(-0.291136\pi\)
\(380\) −1.23607 3.80423i −0.0634089 0.195153i
\(381\) 26.6976 + 19.3969i 1.36776 + 0.993734i
\(382\) 6.47214 4.70228i 0.331143 0.240590i
\(383\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(384\) −9.00000 −0.459279
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 9.27051 28.5317i 0.471246 1.45035i
\(388\) −6.47214 + 4.70228i −0.328573 + 0.238722i
\(389\) 2.42705 + 1.76336i 0.123056 + 0.0894057i 0.647611 0.761971i \(-0.275768\pi\)
−0.524555 + 0.851377i \(0.675768\pi\)
\(390\) 3.70820 + 11.4127i 0.187772 + 0.577903i
\(391\) 0 0
\(392\) −4.85410 3.52671i −0.245169 0.178126i
\(393\) 0 0
\(394\) 4.32624 13.3148i 0.217953 0.670789i
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −12.0000 −0.602263 −0.301131 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 1.85410 5.70634i 0.0929377 0.286033i
\(399\) −29.1246 + 21.1603i −1.45805 + 1.05934i
\(400\) 0.809017 + 0.587785i 0.0404508 + 0.0293893i
\(401\) −11.4336 35.1891i −0.570968 1.75726i −0.649515 0.760349i \(-0.725028\pi\)
0.0785467 0.996910i \(-0.474972\pi\)
\(402\) −12.0517 37.0912i −0.601082 1.84994i
\(403\) 6.47214 + 4.70228i 0.322400 + 0.234237i
\(404\) −4.04508 + 2.93893i −0.201250 + 0.146217i
\(405\) 2.78115 8.55951i 0.138197 0.425325i
\(406\) 18.0000 0.893325
\(407\) 0 0
\(408\) 0 0
\(409\) 6.48936 19.9722i 0.320878 0.987561i −0.652389 0.757884i \(-0.726233\pi\)
0.973267 0.229677i \(-0.0737669\pi\)
\(410\) −4.04508 + 2.93893i −0.199773 + 0.145143i
\(411\) 0 0
\(412\) −2.47214 7.60845i −0.121793 0.374842i
\(413\) 1.85410 + 5.70634i 0.0912344 + 0.280791i
\(414\) −38.8328 28.2137i −1.90853 1.38663i
\(415\) −3.23607 + 2.35114i −0.158852 + 0.115413i
\(416\) −6.18034 + 19.0211i −0.303016 + 0.932588i
\(417\) 54.0000 2.64439
\(418\) 0 0
\(419\) 32.0000 1.56330 0.781651 0.623716i \(-0.214378\pi\)
0.781651 + 0.623716i \(0.214378\pi\)
\(420\) −2.78115 + 8.55951i −0.135706 + 0.417661i
\(421\) −2.42705 + 1.76336i −0.118287 + 0.0859407i −0.645356 0.763882i \(-0.723291\pi\)
0.527069 + 0.849823i \(0.323291\pi\)
\(422\) −17.7984 12.9313i −0.866411 0.629485i
\(423\) −5.56231 17.1190i −0.270449 0.832355i
\(424\) 3.70820 + 11.4127i 0.180086 + 0.554249i
\(425\) 0 0
\(426\) −4.85410 + 3.52671i −0.235182 + 0.170870i
\(427\) 10.1976 31.3849i 0.493495 1.51882i
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) −5.00000 −0.241121
\(431\) 5.56231 17.1190i 0.267927 0.824594i −0.723078 0.690767i \(-0.757273\pi\)
0.991005 0.133827i \(-0.0427268\pi\)
\(432\) −7.28115 + 5.29007i −0.350315 + 0.254518i
\(433\) −11.3262 8.22899i −0.544304 0.395460i 0.281377 0.959597i \(-0.409209\pi\)
−0.825681 + 0.564137i \(0.809209\pi\)
\(434\) −1.85410 5.70634i −0.0889997 0.273913i
\(435\) −5.56231 17.1190i −0.266692 0.820794i
\(436\) −7.28115 5.29007i −0.348704 0.253348i
\(437\) 25.8885 18.8091i 1.23842 0.899763i
\(438\) −7.41641 + 22.8254i −0.354370 + 1.09064i
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 20.2254 14.6946i 0.960939 0.698163i 0.00757032 0.999971i \(-0.497590\pi\)
0.953369 + 0.301808i \(0.0975903\pi\)
\(444\) 19.4164 + 14.1068i 0.921462 + 0.669481i
\(445\) 0.309017 + 0.951057i 0.0146488 + 0.0450844i
\(446\) −1.54508 4.75528i −0.0731619 0.225169i
\(447\) −41.2599 29.9770i −1.95152 1.41787i
\(448\) 16.9894 12.3435i 0.802672 0.583175i
\(449\) −4.01722 + 12.3637i −0.189584 + 0.583481i −0.999997 0.00237857i \(-0.999243\pi\)
0.810413 + 0.585859i \(0.199243\pi\)
\(450\) −6.00000 −0.282843
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 12.9787 39.9444i 0.609793 1.87675i
\(454\) −0.809017 + 0.587785i −0.0379690 + 0.0275861i
\(455\) 9.70820 + 7.05342i 0.455128 + 0.330670i
\(456\) −11.1246 34.2380i −0.520958 1.60334i
\(457\) 8.03444 + 24.7275i 0.375835 + 1.15670i 0.942913 + 0.333038i \(0.108074\pi\)
−0.567078 + 0.823664i \(0.691926\pi\)
\(458\) −0.809017 0.587785i −0.0378029 0.0274654i
\(459\) 0 0
\(460\) 2.47214 7.60845i 0.115264 0.354746i
\(461\) 7.00000 0.326023 0.163011 0.986624i \(-0.447879\pi\)
0.163011 + 0.986624i \(0.447879\pi\)
\(462\) 0 0
\(463\) −15.0000 −0.697109 −0.348555 0.937288i \(-0.613327\pi\)
−0.348555 + 0.937288i \(0.613327\pi\)
\(464\) −1.85410 + 5.70634i −0.0860745 + 0.264910i
\(465\) −4.85410 + 3.52671i −0.225104 + 0.163547i
\(466\) −19.4164 14.1068i −0.899448 0.653487i
\(467\) 8.34346 + 25.6785i 0.386089 + 1.18826i 0.935687 + 0.352831i \(0.114781\pi\)
−0.549598 + 0.835429i \(0.685219\pi\)
\(468\) −7.41641 22.8254i −0.342824 1.05510i
\(469\) −31.5517 22.9236i −1.45692 1.05851i
\(470\) −2.42705 + 1.76336i −0.111952 + 0.0813375i
\(471\) 7.41641 22.8254i 0.341730 1.05174i
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) 30.0000 1.37795
\(475\) 1.23607 3.80423i 0.0567147 0.174550i
\(476\) 0 0
\(477\) −19.4164 14.1068i −0.889016 0.645908i
\(478\) −1.23607 3.80423i −0.0565364 0.174001i
\(479\) 1.85410 + 5.70634i 0.0847161 + 0.260729i 0.984437 0.175736i \(-0.0562303\pi\)
−0.899721 + 0.436465i \(0.856230\pi\)
\(480\) −12.1353 8.81678i −0.553896 0.402429i
\(481\) 25.8885 18.8091i 1.18042 0.857622i
\(482\) −7.10739 + 21.8743i −0.323733 + 0.996347i
\(483\) −72.0000 −3.27611
\(484\) 0 0
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) 6.47214 4.70228i 0.293280 0.213081i −0.431409 0.902157i \(-0.641983\pi\)
0.724689 + 0.689076i \(0.241983\pi\)
\(488\) 26.6976 + 19.3969i 1.20854 + 0.878057i
\(489\) 15.7599 + 48.5039i 0.712686 + 2.19342i
\(490\) −0.618034 1.90211i −0.0279199 0.0859287i
\(491\) −17.7984 12.9313i −0.803229 0.583580i 0.108630 0.994082i \(-0.465354\pi\)
−0.911860 + 0.410502i \(0.865354\pi\)
\(492\) 12.1353 8.81678i 0.547100 0.397491i
\(493\) 0 0
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −1.85410 + 5.70634i −0.0831678 + 0.255964i
\(498\) −9.70820 + 7.05342i −0.435035 + 0.316071i
\(499\) 33.9787 + 24.6870i 1.52110 + 1.10514i 0.960941 + 0.276753i \(0.0892585\pi\)
0.560155 + 0.828388i \(0.310742\pi\)
\(500\) −0.309017 0.951057i −0.0138197 0.0425325i
\(501\) 6.48936 + 19.9722i 0.289923 + 0.892292i
\(502\) 14.5623 + 10.5801i 0.649948 + 0.472215i
\(503\) −10.5172 + 7.64121i −0.468940 + 0.340705i −0.797028 0.603942i \(-0.793596\pi\)
0.328088 + 0.944647i \(0.393596\pi\)
\(504\) −16.6869 + 51.3571i −0.743294 + 2.28762i
\(505\) −5.00000 −0.222497
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −3.39919 + 10.4616i −0.150815 + 0.464159i
\(509\) −18.6074 + 13.5191i −0.824758 + 0.599222i −0.918071 0.396415i \(-0.870254\pi\)
0.0933133 + 0.995637i \(0.470254\pi\)
\(510\) 0 0
\(511\) 7.41641 + 22.8254i 0.328083 + 1.00973i
\(512\) 3.39919 + 10.4616i 0.150224 + 0.462343i
\(513\) 29.1246 + 21.1603i 1.28588 + 0.934249i
\(514\) −4.85410 + 3.52671i −0.214105 + 0.155557i
\(515\) 2.47214 7.60845i 0.108935 0.335268i
\(516\) 15.0000 0.660338
\(517\) 0 0
\(518\) −24.0000 −1.05450
\(519\) −22.2492 + 68.4761i −0.976633 + 3.00577i
\(520\) −9.70820 + 7.05342i −0.425733 + 0.309313i
\(521\) −12.1353 8.81678i −0.531655 0.386270i 0.289321 0.957232i \(-0.406570\pi\)
−0.820977 + 0.570962i \(0.806570\pi\)
\(522\) −11.1246 34.2380i −0.486911 1.49856i
\(523\) −1.23607 3.80423i −0.0540495 0.166347i 0.920388 0.391007i \(-0.127873\pi\)
−0.974437 + 0.224659i \(0.927873\pi\)
\(524\) 0 0
\(525\) −7.28115 + 5.29007i −0.317776 + 0.230877i
\(526\) −3.70820 + 11.4127i −0.161685 + 0.497616i
\(527\) 0 0
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) −1.23607 + 3.80423i −0.0536914 + 0.165245i
\(531\) 9.70820 7.05342i 0.421300 0.306092i
\(532\) −9.70820 7.05342i −0.420904 0.305805i
\(533\) −6.18034 19.0211i −0.267700 0.823897i
\(534\) 0.927051 + 2.85317i 0.0401174 + 0.123469i
\(535\) −7.28115 5.29007i −0.314792 0.228710i
\(536\) 31.5517 22.9236i 1.36282 0.990150i
\(537\) 24.1033 74.1824i 1.04014 3.20121i
\(538\) −21.0000 −0.905374
\(539\) 0 0
\(540\) 9.00000 0.387298
\(541\) 9.57953 29.4828i 0.411856 1.26756i −0.503177 0.864183i \(-0.667836\pi\)
0.915033 0.403379i \(-0.132164\pi\)
\(542\) 0 0
\(543\) −46.1140 33.5038i −1.97894 1.43778i
\(544\) 0 0
\(545\) −2.78115 8.55951i −0.119132 0.366649i
\(546\) 29.1246 + 21.1603i 1.24642 + 0.905576i
\(547\) −29.1246 + 21.1603i −1.24528 + 0.904748i −0.997938 0.0641809i \(-0.979557\pi\)
−0.247340 + 0.968929i \(0.579557\pi\)
\(548\) 0 0
\(549\) −66.0000 −2.81681
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 22.2492 68.4761i 0.946990 2.91454i
\(553\) 24.2705 17.6336i 1.03209 0.749855i
\(554\) 11.3262 + 8.22899i 0.481206 + 0.349616i
\(555\) 7.41641 + 22.8254i 0.314809 + 0.968882i
\(556\) 5.56231 + 17.1190i 0.235894 + 0.726008i
\(557\) 22.6525 + 16.4580i 0.959816 + 0.697347i 0.953108 0.302630i \(-0.0978647\pi\)
0.00670815 + 0.999978i \(0.497865\pi\)
\(558\) −9.70820 + 7.05342i −0.410981 + 0.298595i
\(559\) 6.18034 19.0211i 0.261401 0.804508i
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 6.48936 19.9722i 0.273494 0.841727i −0.716120 0.697977i \(-0.754084\pi\)
0.989614 0.143750i \(-0.0459162\pi\)
\(564\) 7.28115 5.29007i 0.306592 0.222752i
\(565\) −4.85410 3.52671i −0.204214 0.148370i
\(566\) 4.01722 + 12.3637i 0.168856 + 0.519687i
\(567\) −8.34346 25.6785i −0.350392 1.07840i
\(568\) −4.85410 3.52671i −0.203674 0.147978i
\(569\) 8.89919 6.46564i 0.373073 0.271054i −0.385411 0.922745i \(-0.625940\pi\)
0.758484 + 0.651691i \(0.225940\pi\)
\(570\) 3.70820 11.4127i 0.155320 0.478024i
\(571\) −18.0000 −0.753277 −0.376638 0.926360i \(-0.622920\pi\)
−0.376638 + 0.926360i \(0.622920\pi\)
\(572\) 0 0
\(573\) −24.0000 −1.00261
\(574\) −4.63525 + 14.2658i −0.193472 + 0.595445i
\(575\) 6.47214 4.70228i 0.269907 0.196099i
\(576\) −33.9787 24.6870i −1.41578 1.02862i
\(577\) 4.32624 + 13.3148i 0.180104 + 0.554302i 0.999830 0.0184538i \(-0.00587434\pi\)
−0.819726 + 0.572756i \(0.805874\pi\)
\(578\) 5.25329 + 16.1680i 0.218508 + 0.672499i
\(579\) −24.2705 17.6336i −1.00865 0.732826i
\(580\) 4.85410 3.52671i 0.201556 0.146439i
\(581\) −3.70820 + 11.4127i −0.153842 + 0.473478i
\(582\) −24.0000 −0.994832
\(583\) 0 0
\(584\) −24.0000 −0.993127
\(585\) 7.41641 22.8254i 0.306631 0.943712i
\(586\) −27.5066 + 19.9847i −1.13629 + 0.825560i
\(587\) −16.9894 12.3435i −0.701226 0.509470i 0.179105 0.983830i \(-0.442680\pi\)
−0.880331 + 0.474360i \(0.842680\pi\)
\(588\) 1.85410 + 5.70634i 0.0764619 + 0.235325i
\(589\) −2.47214 7.60845i −0.101863 0.313501i
\(590\) −1.61803 1.17557i −0.0666134 0.0483975i
\(591\) −33.9787 + 24.6870i −1.39770 + 1.01549i
\(592\) 2.47214 7.60845i 0.101604 0.312705i
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.25329 16.1680i 0.215183 0.662265i
\(597\) −14.5623 + 10.5801i −0.595996 + 0.433016i
\(598\) −25.8885 18.8091i −1.05866 0.769162i
\(599\) 7.41641 + 22.8254i 0.303026 + 0.932619i 0.980406 + 0.196986i \(0.0631152\pi\)
−0.677380 + 0.735633i \(0.736885\pi\)
\(600\) −2.78115 8.55951i −0.113540 0.349440i
\(601\) 1.61803 + 1.17557i 0.0660010 + 0.0479525i 0.620297 0.784367i \(-0.287012\pi\)
−0.554296 + 0.832320i \(0.687012\pi\)
\(602\) −12.1353 + 8.81678i −0.494596 + 0.359345i
\(603\) −24.1033 + 74.1824i −0.981563 + 3.02094i
\(604\) 14.0000 0.569652
\(605\) 0 0
\(606\) −15.0000 −0.609333
\(607\) −12.3607 + 38.0423i −0.501705 + 1.54409i 0.304537 + 0.952501i \(0.401498\pi\)
−0.806241 + 0.591587i \(0.798502\pi\)
\(608\) 16.1803 11.7557i 0.656199 0.476757i
\(609\) −43.6869 31.7404i −1.77028 1.28619i
\(610\) 3.39919 + 10.4616i 0.137629 + 0.423579i
\(611\) −3.70820 11.4127i −0.150018 0.461708i
\(612\) 0 0
\(613\) 17.7984 12.9313i 0.718870 0.522289i −0.167153 0.985931i \(-0.553457\pi\)
0.886023 + 0.463642i \(0.153457\pi\)
\(614\) 2.47214 7.60845i 0.0997673 0.307052i
\(615\) 15.0000 0.604858
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 7.41641 22.8254i 0.298332 0.918170i
\(619\) 6.47214 4.70228i 0.260137 0.189001i −0.450070 0.892993i \(-0.648601\pi\)
0.710207 + 0.703992i \(0.248601\pi\)
\(620\) −1.61803 1.17557i −0.0649818 0.0472120i
\(621\) 22.2492 + 68.4761i 0.892831 + 2.74785i
\(622\) −7.41641 22.8254i −0.297371 0.915213i
\(623\) 2.42705 + 1.76336i 0.0972377 + 0.0706474i
\(624\) −9.70820 + 7.05342i −0.388639 + 0.282363i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) −8.00000 −0.319744
\(627\) 0 0
\(628\) 8.00000 0.319235
\(629\) 0 0
\(630\) −14.5623 + 10.5801i −0.580176 + 0.421523i
\(631\) 35.5967 + 25.8626i 1.41708 + 1.02957i 0.992244 + 0.124303i \(0.0396696\pi\)
0.424840 + 0.905269i \(0.360330\pi\)
\(632\) 9.27051 + 28.5317i 0.368761 + 1.13493i
\(633\) 20.3951 + 62.7697i 0.810633 + 2.49487i
\(634\) 14.5623 + 10.5801i 0.578343 + 0.420191i
\(635\) −8.89919 + 6.46564i −0.353153 + 0.256581i
\(636\) 3.70820 11.4127i 0.147040 0.452542i
\(637\) 8.00000 0.316972
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0.927051 2.85317i 0.0366449 0.112781i
\(641\) 11.3262 8.22899i 0.447360 0.325026i −0.341193 0.939993i \(-0.610831\pi\)
0.788552 + 0.614968i \(0.210831\pi\)
\(642\) −21.8435 15.8702i −0.862093 0.626347i
\(643\) 10.8156 + 33.2870i 0.426525 + 1.31271i 0.901526 + 0.432725i \(0.142448\pi\)
−0.475001 + 0.879985i \(0.657552\pi\)
\(644\) −7.41641 22.8254i −0.292247 0.899445i
\(645\) 12.1353 + 8.81678i 0.477825 + 0.347160i
\(646\) 0 0
\(647\) −7.72542 + 23.7764i −0.303718 + 0.934747i 0.676435 + 0.736503i \(0.263524\pi\)
−0.980153 + 0.198245i \(0.936476\pi\)
\(648\) 27.0000 1.06066
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) −5.56231 + 17.1190i −0.218004 + 0.670947i
\(652\) −13.7533 + 9.99235i −0.538620 + 0.391331i
\(653\) 27.5066 + 19.9847i 1.07642 + 0.782062i 0.977054 0.212990i \(-0.0683201\pi\)
0.0993611 + 0.995051i \(0.468320\pi\)
\(654\) −8.34346 25.6785i −0.326255 1.00411i
\(655\) 0 0
\(656\) −4.04508 2.93893i −0.157934 0.114746i
\(657\) 38.8328 28.2137i 1.51501 1.10072i
\(658\) −2.78115 + 8.55951i −0.108421 + 0.333684i
\(659\) −42.0000 −1.63609 −0.818044 0.575156i \(-0.804941\pi\)
−0.818044 + 0.575156i \(0.804941\pi\)
\(660\) 0 0
\(661\) −37.0000 −1.43913 −0.719567 0.694423i \(-0.755660\pi\)
−0.719567 + 0.694423i \(0.755660\pi\)
\(662\) 6.18034 19.0211i 0.240206 0.739277i
\(663\) 0 0
\(664\) −9.70820 7.05342i −0.376751 0.273726i
\(665\) −3.70820 11.4127i −0.143798 0.442565i
\(666\) 14.8328 + 45.6507i 0.574760 + 1.76893i
\(667\) 38.8328 + 28.2137i 1.50361 + 1.09244i
\(668\) −5.66312 + 4.11450i −0.219113 + 0.159195i
\(669\) −4.63525 + 14.2658i −0.179209 + 0.551550i
\(670\) 13.0000 0.502234
\(671\) 0 0
\(672\) −45.0000 −1.73591
\(673\) −3.09017 + 9.51057i −0.119117 + 0.366605i −0.992784 0.119920i \(-0.961736\pi\)
0.873666 + 0.486526i \(0.161736\pi\)
\(674\) −9.70820 + 7.05342i −0.373946 + 0.271688i
\(675\) 7.28115 + 5.29007i 0.280252 + 0.203615i
\(676\) −0.927051 2.85317i −0.0356558 0.109737i
\(677\) −8.65248 26.6296i −0.332542 1.02346i −0.967920 0.251257i \(-0.919156\pi\)
0.635379 0.772201i \(-0.280844\pi\)
\(678\) −14.5623 10.5801i −0.559262 0.406328i
\(679\) −19.4164 + 14.1068i −0.745133 + 0.541371i
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 47.0000 1.79841 0.899203 0.437533i \(-0.144148\pi\)
0.899203 + 0.437533i \(0.144148\pi\)
\(684\) −7.41641 + 22.8254i −0.283573 + 0.872749i
\(685\) 0 0
\(686\) 12.1353 + 8.81678i 0.463326 + 0.336626i
\(687\) 0.927051 + 2.85317i 0.0353692 + 0.108855i
\(688\) −1.54508 4.75528i −0.0589058 0.181293i
\(689\) −12.9443 9.40456i −0.493137 0.358285i
\(690\) 19.4164 14.1068i 0.739170 0.537038i
\(691\) −12.3607 + 38.0423i −0.470222 + 1.44720i 0.382072 + 0.924133i \(0.375211\pi\)
−0.852294 + 0.523063i \(0.824789\pi\)
\(692\) −24.0000 −0.912343
\(693\) 0 0
\(694\) −7.00000 −0.265716
\(695\) −5.56231 + 17.1190i −0.210990 + 0.649361i
\(696\) 43.6869 31.7404i 1.65595 1.20312i
\(697\) 0 0
\(698\) −6.79837 20.9232i −0.257322 0.791956i
\(699\) 22.2492 + 68.4761i 0.841543 + 2.59000i
\(700\) −2.42705 1.76336i −0.0917339 0.0666486i
\(701\) −30.7426 + 22.3358i −1.16113 + 0.843613i −0.989921 0.141621i \(-0.954769\pi\)
−0.171213 + 0.985234i \(0.554769\pi\)
\(702\) 11.1246 34.2380i 0.419871 1.29223i
\(703\) −32.0000 −1.20690
\(704\) 0 0
\(705\) 9.00000 0.338960
\(706\) −1.85410 + 5.70634i −0.0697800 + 0.214761i
\(707\) −12.1353 + 8.81678i −0.456393 + 0.331589i
\(708\) 4.85410 + 3.52671i 0.182428 + 0.132542i
\(709\) −7.72542 23.7764i −0.290134 0.892942i −0.984813 0.173621i \(-0.944453\pi\)
0.694678 0.719321i \(-0.255547\pi\)
\(710\) −0.618034 1.90211i −0.0231944 0.0713850i
\(711\) −48.5410 35.2671i −1.82043 1.32262i
\(712\) −2.42705 + 1.76336i −0.0909576 + 0.0660846i
\(713\) 4.94427 15.2169i 0.185164 0.569878i
\(714\) 0 0
\(715\) 0 0
\(716\) 26.0000 0.971666
\(717\) −3.70820 + 11.4127i −0.138485 + 0.426214i
\(718\) −22.6525 + 16.4580i −0.845383 + 0.614207i
\(719\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(720\) −1.85410 5.70634i −0.0690983 0.212663i
\(721\) −7.41641 22.8254i −0.276201 0.850061i
\(722\) −2.42705 1.76336i −0.0903255 0.0656253i
\(723\) 55.8222 40.5572i 2.07605 1.50834i
\(724\) 5.87132 18.0701i 0.218206 0.671569i
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) −11.1246 + 34.2380i −0.412306 + 1.26895i
\(729\) 21.8435 15.8702i 0.809017 0.587785i
\(730\) −6.47214 4.70228i −0.239544 0.174039i
\(731\) 0 0
\(732\) −10.1976 31.3849i −0.376913 1.16002i
\(733\) −29.1246 21.1603i −1.07574 0.781572i −0.0988065 0.995107i \(-0.531502\pi\)
−0.976936 + 0.213534i \(0.931502\pi\)
\(734\) 0.809017 0.587785i 0.0298614 0.0216955i
\(735\) −1.85410 + 5.70634i −0.0683896 + 0.210481i
\(736\) 40.0000 1.47442
\(737\) 0 0
\(738\) 30.0000 1.10432
\(739\) −3.09017 + 9.51057i −0.113674 + 0.349852i −0.991668 0.128819i \(-0.958881\pi\)
0.877994 + 0.478671i \(0.158881\pi\)
\(740\) −6.47214 + 4.70228i −0.237920 + 0.172859i
\(741\) 38.8328 + 28.2137i 1.42656 + 1.03646i
\(742\) 3.70820 + 11.4127i 0.136132 + 0.418973i
\(743\) −2.16312 6.65740i −0.0793571 0.244236i 0.903505 0.428577i \(-0.140985\pi\)
−0.982862 + 0.184341i \(0.940985\pi\)
\(744\) −14.5623 10.5801i −0.533880 0.387887i
\(745\) 13.7533 9.99235i 0.503882 0.366091i
\(746\) −5.56231 + 17.1190i −0.203650 + 0.626772i
\(747\) 24.0000 0.878114
\(748\) 0 0
\(749\) −27.0000 −0.986559
\(750\) 0.927051 2.85317i 0.0338511 0.104183i
\(751\) −8.09017 + 5.87785i −0.295214 + 0.214486i −0.725526 0.688194i \(-0.758404\pi\)
0.430312 + 0.902680i \(0.358404\pi\)
\(752\) −2.42705 1.76336i −0.0885054 0.0643030i
\(753\) −16.6869 51.3571i −0.608105 1.87156i
\(754\) −7.41641 22.8254i −0.270090 0.831250i
\(755\) 11.3262 + 8.22899i 0.412204 + 0.299484i
\(756\) 21.8435 15.8702i 0.794439 0.577194i
\(757\) −3.70820 + 11.4127i −0.134777 + 0.414801i −0.995555 0.0941792i \(-0.969977\pi\)
0.860778 + 0.508980i \(0.169977\pi\)
\(758\) 22.0000 0.799076
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) 8.03444 24.7275i 0.291248 0.896370i −0.693208 0.720738i \(-0.743803\pi\)
0.984456 0.175632i \(-0.0561969\pi\)
\(762\) −26.6976 + 19.3969i −0.967151 + 0.702676i
\(763\) −21.8435 15.8702i −0.790786 0.574540i
\(764\) −2.47214 7.60845i −0.0894387 0.275264i
\(765\) 0 0
\(766\) 0 0
\(767\) 6.47214 4.70228i 0.233695 0.169790i
\(768\) 15.7599 48.5039i 0.568685 1.75023i
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 3.09017 9.51057i 0.111218 0.342293i
\(773\) 17.7984 12.9313i 0.640163 0.465106i −0.219743 0.975558i \(-0.570522\pi\)
0.859906 + 0.510452i \(0.170522\pi\)
\(774\) 24.2705 + 17.6336i 0.872385 + 0.633825i
\(775\) −0.618034 1.90211i −0.0222004 0.0683259i
\(776\) −7.41641 22.8254i −0.266234 0.819383i
\(777\) 58.2492 + 42.3205i 2.08968 + 1.51824i
\(778\) −2.42705 + 1.76336i −0.0870140 + 0.0632194i
\(779\) −6.18034 + 19.0211i −0.221434 + 0.681503i
\(780\) 12.0000 0.429669
\(781\) 0 0